We present some applications of geometric optimal control theory
to control problems in Nuclear Magnetic Resonance (NMR) and
Magnetic Resonance Imaging (MRI). Using the Pontryagin Maximum
Principle (PMP), the optimal trajectories are found as solutions
of a pseudo-Hamiltonian system. This computation can be completed
by second-order optimality conditions based on the concept of
conjugate points. After a brief physical introduction to NMR, this
approach is applied to analyze two relevant optimal control issues
in NMR and MRI: the control of a spin 1/2 particle in presence of
radiation damping effect and the maximization of the contrast in
MRI. The theoretical analysis is completed by numerical
computations. This work has been made possible by the central and
essential role of B. Bonnard, who has been at the heart of this
project since 2009.

R. R. Ernst, G. Bodenhausen and A. Wokaun, "Principles of Nuclear Magnetic Resonance in One and Two Dimensions,", International Series of Monographs on Chemistry, (1990).
doi: 10.1063/1.2811094. Google Scholar

R. R. Ernst, G. Bodenhausen and A. Wokaun, "Principles of Nuclear Magnetic Resonance in One and Two Dimensions,", International Series of Monographs on Chemistry, (1990).
doi: 10.1063/1.2811094. Google Scholar